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Wan Doy Pairs Poker

Introduction

Wan Doy is a unique poker-based game using seven cards, with no straights or flushes. Although the rules are unconventional the optimal strategy is simple and the element of risk is 1.94%. The game is available to play at online casinos using Wager Works software.

Rules

The game is played with a single 52-card deck, which is shuffled before every hand. All cards are ranked as in poker, except aces are always high.

Play starts with the player making an ante and Bonus Wager of exactly the same amount. In addition there is an optional side bet.

After all wagers have been made each player and the dealer shall receive seven cards dealt face down. The player may look at his own cards but may not share information with other players.

After examining his own cards the player has the choice to either raise or fold. If the player raises he must make a raise wager exactly equal to the ante wager. If the player folds he forfeits the ante, Bonus Wager, side bet (if made), and his cards.

The dealer will flip over his cards.

Both player and dealer hands will be ranked according to the Bonus Wager pay table. Note that there are no straights or flushes. Only pairs and higher shall count for purposes of breaking a tie. For example QQ66J83 would beat QQ44K97. Singletons are not considered in the ranking of hands. For example KKQ9753 would push against KKJ9753. Any two hands of less than a pair would push.

If the player hand outranks the dealer hand then the ante and raise bets shall pay even money.

If the player has at least a three of a kind then the bonus hand shall pay according to Bonus Wager Pay Table below, regardless of the value of the dealer hand.

If the player has less than a three of a kind and the player beats the dealer then the Bonus Wager shall push. Otherwise if the player has less than a three of a kind and ties or loses to the dealer's hand then the bonus bet shall lose.

The side bet shall pay according to both the value of player's and dealer's hands. If both hands qualify for a win then the player will be paid for both. If one hand qualifies for a win the player's original side shall be returned, if both qualify the player shall get his original side bet back twice.

The following pay table is for the Bonus Wager.

Bonus Wager Pay Table

Hand

Pays

Four of a kind plus Three of a kind

100

Four of a kind plus pair

80

2 Three of a kinds

50

Three of a kind plus 2 pairs

25

Four of kind

10

3 pairs

5

Three of a kind plus pair

3

Three of a kind

2

2 pair or less, player beats dealer

0

2 pair or less, dealer ties or beats player

-1

The following pay table is the last known confirmed one for the side bet, which pays based on both the player's and dealer's hand. The original bet is returned once for each win.

Side Bet Pay Table

Hand

Pays

4 of a kind + 3 of a kind

5000

4 of a kind + pair

150

3 of a kind + 3 of a kind

75

3 of a kind + pair + pair

50

4 of a kind

20

Pair + pair + pair

15

All other

Loss

House Edge

The following table shows all possible outcomes under optimal player strategy, the win (positive) or loss (negative) to the player, the probability, and contribution to the total return.

Wan Doy Return Table

Player Hand

Winner

Pays

Combinations

Probability

Return

4 of a kind + 3 of a kind

Player

102

28316700000

0.000005

0.000476

4 of a kind + pair

Player

82

1868460000000

0.000308

0.025237

3 of a kind + 3 of a kind

Player

52

2489930000000

0.00041

0.021327

3 of a kind + pair + pair

Player

27

5597370000000

0.000922

0.024893

4 of a kind

Player

12

8280440000000

0.001364

0.016367

Pair + pair + pair

Player

7

110621000000000

0.018221

0.127546

3 of a kind + pair

Player

5

143704000000000

0.02367

0.118351

3 of a kind

Player

4

276136000000000

0.045484

0.181935

Pair + pair

Player

2

1061320000000000

0.174815

0.34963

Pair

Player

2

1272310000000000

0.209568

0.419136

No pair

Player

2

0

0

0

4 of a kind + 3 of a kind

Dealer

98

137280

0

0

4 of a kind + pair

Dealer

78

458172000

0

0.000006

3 of a kind + 3 of a kind

Dealer

48

1953220000

0

0.000015

3 of a kind + pair + pair

Dealer

23

9372650000

0.000002

0.000036

4 of a kind

Dealer

8

25731000000

0.000004

0.000034

Pair + pair + pair

Dealer

3

1513750000000

0.000249

0.000748

3 of a kind + pair

Dealer

1

5809190000000

0.000957

0.000957

3 of a kind

Dealer

0

22890200000000

0.00377

0

Pair + pair

Dealer

-3

284047000000000

0.046787

-0.14036

Pair

Dealer

-3

1569260000000000

0.25848

-0.775441

No pair

Dealer

-3

0

0

0

4 of a kind + 3 of a kind

Tie

100

0

0

0

4 of a kind + pair

Tie

80

0

0

0

3 of a kind + 3 of a kind

Tie

50

0

0

0

3 of a kind + pair + pair

Tie

25

0

0

0

4 of a kind

Tie

10

115150000

0

0

Pair + pair + pair

Tie

5

96370600

0

0

3 of a kind + pair

Tie

3

0

0

0

3 of a kind

Tie

2

0

0

0

Pair + pair

Tie

-1

252254000000

0.000042

-0.000042

Pair

Tie

-1

29086800000000

0.004791

-0.004791

No pair

Tie

-1

0

0

0

Player folds

-2

1275850000000000

0.210151

-0.420303

Total

6071102437399880

1

-0.054243

The lower right cell shows that for two initial bets of 1 unit each the player can expect to lose 0.054243 units. For example if the player bet $100 on the ante and Bonus Wager he could expect to lose $5.42. The house edge is traditionally defined as the expected loss to the initial wager. In this case two initial wagers are required so the house edge would be 5.4243%/2 = 2.7122%. After considering raise bets the average total wager is 2.79 units. Thus the element of risk is 5.4243%/2.79 = 1.94%.

Originally, three pairs paid 6 to 1, as opposed to the current 5 to 1. I think most, if not all Wager Works casinos now pay 5 to 1, so I indicate 5 as the win for three pairs in the pay table above. However, should you see a game that pays 6 to 1 the house edge would be lowered to 3.58%.

The next table shows how the return of the side bet is determined. The side bet is actually two side bets, half on the player's hand and half on the dealer's hand. So for a loss I show only half a unit. Normally the return column is the product of the probability and the win. However in this case it is double that, because there are two hands the bet is based on.

Side Bet Return Table

Hand

Pays

Combinations

Probability

Return

4 of a kind + 3 of a kind

5000

624

0.000005

0.046642

4 of a kind + pair

150

41184

0.000308

0.092351

3 of a kind + 3 of a kind

75

54912

0.00041

0.061568

3 of a kind + pair + pair

50

123552

0.000924

0.092351

4 of a kind

20

183040

0.001368

0.054727

Pair + pair + pair

15

2471040

0.01847

0.554109

All other

-0.5

130910208

0.978515

-0.978515

Total

133784560

1

-0.076767

Strategy

The strategy is simple, the player should raise on any pair or higher.